8 citations · 25 across the 13 of their papers we have counts for
13 papers
Functional Neural Wavefunction Optimization
Victor Armegioiu, Juan Carrasquilla, Siddhartha Mishra +4
We propose a framework for the design and analysis of optimization algorithms in variational quantum Monte Carlo, drawing on geometric insights into the corresponding function spac…
Dynamical Measure Transport and Neural PDE Solvers for Sampling
Jingtong Sun, Julius Berner, Lorenz Richter +4
The task of sampling from a probability density can be approached as transporting a tractable density function to the target, known as dynamical measure transport. In this work, we…
Kronecker-Factored Approximate Curvature for Physics-Informed Neural Networks
Felix Dangel, Johannes Müller, Marius Zeinhofer
Physics-informed neural networks (PINNs) are infamous for being hard to train. Recently, second-order methods based on natural gradient and Gauss-Newton methods have shown promisin…
Position: Optimization in SciML Should Employ the Function Space Geometry
Johannes Müller, Marius Zeinhofer
Scientific machine learning (SciML) is a relatively new field that aims to solve problems from different fields of natural sciences using machine learning tools. It is well-documen…
Achieving High Accuracy with PINNs via Energy Natural Gradients
Johannes Müller, Marius Zeinhofer
We propose energy natural gradient descent, a natural gradient method with respect to a Hessian-induced Riemannian metric as an optimization algorithm for physics-informed neural n…
Three Dimensional Optimization of Scaffold Porosities for Bone Tissue Engineering
Patrick Dondl, Marius Zeinhofer
We consider the scaffold design optimization problem associated to the three dimensional, time dependent model for scaffold mediated bone regeneration considered in Dondl et al. (2…
Regularity for Reaction-Diffusion Equations with Non-smooth Data
Patrick Dondl, Marius Zeinhofer
We prove an regularity result for a reaction-diffusion equation with mixed boundary conditions, symmetric coefficients and an initial conditio…
Uniform Convergence Guarantees for the Deep Ritz Method for Nonlinear Problems
Patrick Dondl, Johannes Müller, Marius Zeinhofer
We provide convergence guarantees for the Deep Ritz Method for abstract variational energies. Our results cover non-linear variational problems such as the -Laplace equation or…
A parameter study on optimal scaffolds in a simple model for bone regeneration
Patrick Dondl, Marius Zeinhofer
We propose a simple model for scaffold aided bone regeneration. In this model, only macroscopic quantities, e.g., locally averaged osteoblast densities, are considered. This allows…
Notes on Exact Boundary Values in Residual Minimisation
Johannes Müller, Marius Zeinhofer
We analyse the difference in convergence mode using exact versus penalised boundary values for the residual minimisation of PDEs with neural network type ansatz functions, as is co…
Error Estimates for the Deep Ritz Method with Boundary Penalty
Johannes Müller, Marius Zeinhofer
We estimate the error of the Deep Ritz Method for linear elliptic equations. For Dirichlet boundary conditions, we estimate the error when the boundary values are imposed through t…
An Efficient Model for Scaffold-Mediated Bone Regeneration
Patrick Dondl, Patrina S. P. Poh, Marius Zeinhofer
We present a three dimensional, time dependent model for bone regeneration in the presence of porous scaffolds to bridge critical size bone defects. Our approach uses homogenized q…
Deep Ritz revisited
Johannes Müller, Marius Zeinhofer
Recently, progress has been made in the application of neural networks to the numerical analysis of partial differential equations (PDEs). In the latter the variational formulation…